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Topological speedups for minimal Cantor systems

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Abstract

In this paper we study speedups of dynamical systems in the topological category. Specifically, we characterize when one minimal homeomorphism on a Cantor space is the speedup of another. We go on to provide a characterization for strong speedups, i.e., when the jump function has at most one point of discontinuity. These results provide topological versions of the measure-theoretic results of Arnoux, Ornstein and Weiss, and are closely related to Giordano, Putnam and Skau’s characterization of orbit equivalence for minimal Cantor systems.

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Acknowledgments

The authors thank the referee for their close reading of our paper and for their insightful suggestions. Additionally, the first author dedicates this paper to Laura Brade. Your unwavering belief in me and support of me made this paper possible. Thank you.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Albion College, 611 E. Porter Street, Albion, MI, 49224, USA

    Drew D. Ash

  2. Department of Mathematics, University of Denver, 2280 S. Vine Street, Denver, CO, 80208, USA

    Nicholas S. Ormes

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  1. Drew D. Ash
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  2. Nicholas S. Ormes
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Correspondence to Drew D. Ash.

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Ash, D.D., Ormes, N.S. Topological speedups for minimal Cantor systems. Isr. J. Math. (2023). https://doi.org/10.1007/s11856-023-2568-7

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  • DOI: https://doi.org/10.1007/s11856-023-2568-7

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